Dynamic Model Analysis Of The Spread Of Infectious Diseases Based On Detection Behavior

The spread of infectious diseases has a great negative impact on the economic devel-opment and public health of epidemic areas.In order to reduce these animal epidemics Many risk management measures are used for the prevention and control of animal diseases,among which,the detection and culling measures are used for the prevention and control of animal diseases.Prevention and control play an important role.Therefore,based on the detection behavior,the animal epidemic transmission dynamics model is established to study the detection behavior on the basis of the detection behavior.The impact of epidemic transmission is the primary task.The completion of the task can provide theoretical basis for the prevention and control of infectious diseases.In the second chapter,based on the specific characteristics of brucellosis detection,a time-delay dynamic model is established.Firstly,the basic reproduction number R₀and the threshold value R_care given.The existence conditions of equilibrium point are analyzed.when R_c<R₀?1,the model has one disease free equilibrium point E₀;when R_c<1<R₀,the model has an endemic equilibrium point E₁^*;when 1<R₀<R_c,the model has an endemic equilibrium point E₂^*.Secondly,the stability of the equilibrium point is analyzed.And by the method of numerical analysis it is found when the?exceeded the critical value,the model would have periodic oscillation,which indicated that the delay in detection time could lead to the periodic fluctuation of the epidemic disease.In the third chapter,a time-lag dynamic model of bovine tuberculosis was established.Bovine tuberculosis can also be transmitted in the latent period.The Chapter does not study the latent person alone,but classifies the latent person as the infectious person.Firstly,the basic reproduction number R₀and the threshold value R_care given.The existence condi-tions of equilibrium point are analyzed.when R_c<R₀?1,the model has one disease free equilibrium point E₀;when R_c<1<R₀,the model has an endemic equilibrium point E₁^*;when 1<R₀<R_c,the model has an endemic equilibrium point E₂^*.Then the stability of the equilibrium point is analyzed and the Hopf bifurcation of the model is obtained by calculation.At last,the numerical simulation is carried out.